Fermion-scalar conformal blocks

@article{Iliesiu2015FermionscalarCB,
  title={Fermion-scalar conformal blocks},
  author={Luca V. Iliesiu and Filip Kos and David Poland and Silviu S. Pufu and David Simmons-Duffin and Ran Yacoby},
  journal={Journal of High Energy Physics},
  year={2015},
  volume={2016},
  pages={1-20}
}
A bstractWe compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators. 
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References

SHOWING 1-10 OF 61 REFERENCES

Bootstrapping 3D fermions

A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in…

Deconstructing conformal blocks in 4D CFT

A bstractWe show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field…

Recursion relations for conformal blocks

A bstractIn the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of the…

Scalar-vector bootstrap

A bstractWe work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field…

Central charge bounds in 4D conformal field theory

TLDR
It is shown that the stress tensor central charge C-T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory.

Radial Coordinates for Conformal Blocks

We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is…

Projectors, shadows, and conformal blocks

A bstractWe introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to…

Bootstrapping the 3d Ising twist defect

A bstractRecent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon…

The superconformal bootstrap for structure constants

A bstractWe report on non-perturbative bounds for structure constants on N=4$$ \mathcal{N}=4 $$ SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to super-conformal…

Bootstrapping the Three Dimensional Supersymmetric Ising Model.

TLDR
The conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry is implemented and universal constraints on the spectrum of operator dimensions in these theories are found.
...